1. Field of the Invention
The invention herein relates to techniques for resolving imaging data collected during geophysical exploration.
2. Description of the Related Art
A number of problems arise during geophysical exploration. For example, resolving seismic wave propagation data in isotropic and anisotropic formations (media) has required elaborate modeling. One model is that of the Kirchhoff migration model.
The traveltime calculation is the backbone of any Kirchhoff pre-stack depth migration. During the past decade, there have been numerous methods developed based upon the eikonal equation solver to calculate traveltimes in three dimensional (3D) isotropic media. Those methods are generally classified as either ray tracing or finite difference (FD) approaches.
Among them, one approach is the fast marching algorithm with first or higher order FD eikonal equation solver. This method has proven popular due to its computation efficiency, stability, and satisfactory accuracy (Popovici and Sethian 2002). It has been well recognized however, that most sedimentary rocks display transverse isotropy (TI) with a vertical symmetry axis (VTI) or a general tilted symmetric axis (TTI) to seismic waves. The phenomena can significantly affect focusing and imaging positions in seismic data migration. Recently, Alkhalifah (2002) presented a FD algorithm to solve first arrival traveltimes in 3D VTI media by a perturbation method. Jiao (2005) used a similar FD algorithm based on perturbation theory to calculate first arrival traveltimes in 3D TTI media. In addition, Zhang et. al. (2002) presented a FD scheme in the celerity domain to calculate first arrival traveltimes in 2D TTI media.
What are lacking are improvements to efficiency, accuracy and stability in order to reduce the costs associated with geological exploration.